A successive convexification approach for robust receding horizon control

Abstract: A novel robust nonlinear model predictive control strategy is proposed for systems with nonlinear dynamics and convex state and control constraints. Using a sequential convex approximation approach and a difference of convex functions representation, the scheme constructs tubes that contain predicted model trajectories, accounting for approximation errors and disturbances, and guaranteeing constraint satisfaction. An optimal control problem is solved as a sequence of convex programs. We develop the scheme initially in the absence of external disturbances and show that the proposed nominal approach is non-conservative, with the solutions of successive convex programs converging to a locally optimal solution for the original optimal control problem. We extend the approach to the case of additive disturbances using a novel strategy for selecting linearization points. As a result we formulate a robust receding horizon strategy with guarantees of recursive feasibility closed-loop system stability.